Basic Trig

FunctionsAn Introduction to Sine,

Cosine, and Tangent

Melanie Forbes

Mosque Detail, provided by Let’s Book (Jamie Carter) on Flickr, Creative Commons, some rights reserved, April 2009, Seoul, Korea.

What are Trig Functions?

Let’s look at 3 similar triangles

If the angles of one triangle are exactly the

same as the angles of another, those

triangles are similar.

3

4

5

θ

β

6

8

10

θ

β

4.5

6

7.5

θ

β

These are 3 similar right triangles;

they each have a 90° angle,

equal angles θ, and equal

angles β.

Comparing Sides

3

4

5

θ

β

Comparing Sides

4.5

6

7.5

θ

β

Ratios are the Same

Did you notice that each of the 3 similar

triangles, even though the triangles were

different sizes, had the exact same ratio

of sides?

Comparing Sides

6

8

10

θ

β

The Sine Function

3

4

5

θ

β

Mosaic Tile Medallion, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.

Practice

In each triangle, determine sine θ.

Just click to see the correct answer

What is Sine θ?

7

2425

θ

What is Sine θ?

9

40

41θ

What is Sine θ?

5

12

13

θ

How did you do?

If you correctly identified the sine ratios in

those triangles, click to move to the next

section.

Otherwise, click below to go back.

Go to the beginning Review the sine ratio

Left Arrows Reverse Button, Provided by: Microsoft

Decorative and Calligraphic Tilewormk, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.

The Cosine Function

3

4

5

θ

β

Practice

In each triangle, determine cosine θ.

Just click to see the correct answer

What is Cosine θ?

7

2425

θ

What is Cosine θ?

9

40

41θ

What is Cosine θ?

5

12

13

θ

How did you do?

If you correctly identified the cosine ratios

in those triangles, click to move to the

next section.

Otherwise, click below to go back.

Review the sine ratio Review the cosine ratio

Left Arrows Reverse Button, Provided by: Microsoft

3D Ornamental Mosaic Tile, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Kerman, Iran

The Tangent Ratio

3

4

5

θ

β

Practice

In each triangle, determine tangent θ.

Just click to see the correct answer

What is Tangent θ?

7

2425

θ

What is Tangent θ?

9

40

41θ

What is Tangent θ?

5

12

13

θ

How did you do?

If you correctly identified the tangent

ratios in those triangles, click to move to

the next section.

Otherwise, click below to go back.

Review the cosine ratio Review the tangent ratio

Left Arrows Reverse Button, Provided by: Microsoft

SOH – CAH - TOA You can remember the definitions of the 3

trig ratios with a mnemonic

SOH: Sin=Opposite/Hypotenuse

CAH: Cos=Adjacent/Hypotenuse

TOA: Tan=Opposite/Adjacent

Detail 3-D Tilework, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.

Thanks for

Watching.

Any idea why I included

pictures from the Middle East?

Detail 3-D Tilework, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.